Reaction-diffusion-advection Models for Single and Multiple Species

Download or read book Reaction-diffusion-advection Models for Single and Multiple Species written by Andriy Bezuglyy and published by . This book was released on 2009 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The dispersal of organisms in a heterogeneous environment is rarely random as individuals can sense and respond to local environmental cues by moving towards favorable habitats. We study reaction-diffusion-advection models which describe the biased movement of species upward along the resource gradient. Our focus is on the effects of such non-random movement of organisms on the spatial distribution and dynamics of populations. For a single species at equilibrium, previous works show that the species with strong biased movement upward along the resource gradient will overmatch the resource at each global maximum of the resource. In this work we show that, in fact, the species will overmatch the resource at each local maximum of the resource. As an application, we also study a reaction-diffusion-advection model for two competing species. We assume that the two species are identical except for their dispersal strategies: Both species adopt random dispersal combined with the advection upward along the resource gradient. It was shown in previous works thatwhen both advection rates are large, a competitive exclusion phenomenon occurs: The species with relatively weaker advection drives the other to extinction, under the assumption that the resource has a unique maximum. In this work we extend this competitive exclusion result to general resource functions with finite but arbitrarily many of local maxima.